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<p>One kind of approach, which we called “equivalent cost functional method” is introduced by Yu (ESAIM Control Optim Calc Var. 2013;19:78–90) in the setup of Hamilton system, is applied to get a solvability of a stochastic linear quadratic (SLQ for short) optimal control problem with random jumps and indefinite control weight costs in a finite time horizon. Our analysis is featured by some equivalent cost functionals which enable us to transform the indefinite SLQ problems to positive-definite case, it is remarkable that the solvability of the former is rather complicated than the latter. Consequently, the indefinite SLQ optimal control problem with random jumps is discussed and an explicit state feedback representation of the indefinite SLQ optimal control problem with random jumps is given by the solution of associated indefinite stochastic Riccati equation(SRE for short). </p>

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Solvability of Indefinite Stochastic LQ Optimal Control Problems for Jump Diffusion Models

  • 期刊论文

  • 发表日期：

    2026年2月7日

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  • Chao Tang,
  • Xueqin Li,
  • Qi Wang

摘要

One kind of approach, which we called “equivalent cost functional method” is introduced by Yu (ESAIM Control Optim Calc Var. 2013;19:78–90) in the setup of Hamilton system, is applied to get a solvability of a stochastic linear quadratic (SLQ for short) optimal control problem with random jumps and indefinite control weight costs in a finite time horizon. Our analysis is featured by some equivalent cost functionals which enable us to transform the indefinite SLQ problems to positive-definite case, it is remarkable that the solvability of the former is rather complicated than the latter. Consequently, the indefinite SLQ optimal control problem with random jumps is discussed and an explicit state feedback representation of the indefinite SLQ optimal control problem with random jumps is given by the solution of associated indefinite stochastic Riccati equation(SRE for short).